Alternative interpretations of the many-particle Lippmann-Schwinger equation

Journal Article · Tue Jul 01 04:00:00 EDT 1986 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.34.1· OSTI ID:5568218

Gerjuoy, E; Adhikari, S K

Possible alternative interpretations of the Lippmann-Schwinger integral equation for multiparticle (n-italic>2) systems are investigated and are shown to be equivalent if integrals which occur are uniformly convergent, as is reasonable. At real energies E-italic, the derivation of the Lippmann-Schwinger equation from the Schroedinger equation involves various surface integrals at infinity in configuration space. It is shown that the values of these surface integrals are related to the values of certain volume integrals at complex energies (E-italic+i-italicepsilon) in the limit epsilon..-->..0, originally examined by Lippmann. It is further proved that a number of these surface integrals vanish together, a result which: though plausible: previously had to be assumed. The results of this paper confirm previous studies showing that the solutions to the multiparticle Lippmann-Schwinger equation need not be unique. Because of certain convergence difficulties which can occur, the analysis of this paper is not wholly valid for ''three-body'' collisions (defined as collisions involving three independently incident aggregates of the fundamental particles comprising the multiparticle system), or for the even more complicated collisions involving n-italic>3 incident aggregates.

• Research Organization: Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
• OSTI ID: 5568218
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 34:1; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
FADDEEV EQUATIONS
FUNCTIONS
GREEN FUNCTION
INTEGRAL EQUATIONS
INTEGRALS
LIPPMANN-SCHWINGER EQUATION
MANY-BODY PROBLEM
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
WAVE EQUATIONS